Boundary element formulation for 2D solids with stiff and soft thin inclusions

In this work, a linear boundary element formulation is presented for analysing solids containing stiff and soft thin inclusions. A particular sub-region technique, in which the equilibrium is preserved along interfaces without traction approximation, is adapted to model thin inclusions as fibres and beams immersed in a solid. An alternative formulation, in which tractions along interfaces are preserved as unknowns, eliminating therefore displacements, is also derived and applied to the analysis of inclusions in 2D solids in general. For the case of thin inclusions, fibres and beams, the displacement field is properly approximate over the cross-sections. The quasi-singular integrals appearing in all presented formulations are computed by using closed expressions or employing a numerical scheme with sub-elements.